.
The solution to the part 1)
Between the 4-th and 7-th terms of any AP, there are 3 gaps of equal size.
Therefore, the common difference is d = = . ANSWER
The solution to the part 2)
Notice that is the 4-th term of the AP from the beginning,
while is the 4-th term of the AP from the end (from the ending term ).
Therefore, = = p + q. (*)
It is a general property of any AP:
the sum of the terms equally remoted from the beginning and the end of an AP
is equal to the sum of the first and the last its terms.
From the other side, the sum of any AP is equal to the sum of the first and the last terms, divided by 2 and multiplied
by the number of terms.
Therefore,
+ + + . . . + = = = = 5*(p+q). ANSWER
Both questions are answered, and the problem is solved.